Two new developments overnight.
1. I tried a different display (23" LCD) on the 2008 and 2009 Mac Pro. The Mini DisplayPort on the 5870 *DOES* work on the both. Furthermore, I have reports from readers that the Mini DisplayPort works fine on their 2006 Mac Pro with the 4870. Therefore, I rescind my caveat that the Mini DisplayPort isn't compatible with the older Mac Pros.
2. I have access to a 2006 Mac Pro in a day or so. I'll be trying the 5870 on it. OWC has the 5770 working on their 2006 but they said the 5870 was a "no." Yet I have another source that says it is working reliably on their 2006. Seems like I remember there being a Boot ROM or SMC difference in the earliest Mac Pros that affected the ability to use the 4870 --- but that should also apply to the 5770. Also in 2007, the 8-core "2006" was released with a different Boot ROM or SMC version. Still digging.